But as with many a question we don’t know the answer to, thinking about them can still be worthwhile in their own right. And I believe there are good arguments indicating that the brain isn’t a quantum computer, so the answer is more like we don’t know, but probably not.

Nevertheless, there are many theories that in some way relate the brain to quantum physics, and the fact that the brain is not a quantum computer does not mean that there could not be quantum effects playing some kind of role in the brain. Parsing through the different perspectives and several layers on this question may seem like a daunting task, but I think on some aspects of it clearer, scientifically more grounded arguments are to be made than on others.

I’ll begin the first half of this article with a computer scientific and evolutionary perspective on the title question. In the second half, I venture down the rabbit hole into the strange and more speculative realm of quantum minds, Schrödinger’s synaptic clefts, and consciousness.

Classical Computers

Classical computers are based on the principles of the Turing machine, which has been shown to be equivalent to all descriptions of classical computational machines (like the lambda-calculus) that people have come up with since the days of Turing. I went at length through how they work and what makes them so powerful here. Turing machines can be implemented in many different ways, but every Turing machine contains something called a tape, on which information is stored and can be read out and manipulated by the head of the machine. This tape stores symbols (like numbers 0 or 1 or letters, words, etc.).

Computation in a Turing machine is equivalent to manipulation of the symbols on the tape, implemented through algorithms. You can, for example, add two numbers with a Turing machine by following a given procedure, the details of which depend on the symbolic language used. After the algorithm is run, an input (the initial state of the tape) is transformed into an output (the state of the tape at the end of the procedure).

While there is some controversy on the question if the brain is indeed a Turing machine, and good reasons to think that it is at least not obviously one (although Turing machines can be implemented in many ways, for example with Recurrent Neural Networks), the main point here is to emphasize that information in Turing machines is stored classically, which means in a way that does not involve quantum bits.

Quantum Computers

Quantum Computers, on the other hand, don’t store information on a tape but encode it in quantum bits. As an example, the spin of an electron or an atom can be used as a qubit. In the same vein as within a Turing machine, the computation in a quantum computer takes place by encoding algorithms as operations on qubits, carrying out these operations, and reading out the desired result, which is found in the final state of the qubit(s).

The Bloch sphere is the place where the qubits live (or, for the technically interested, what happens when you map the pure spin states represented by SU(2) onto the 2-sphere via Hopf fibration).

Quantum computers are more powerful than classical computers in some ways, because qubits, through a special quantum property called superposition, are more “expressive” than simple bits and can hold more information (especially the combination of multiple qubits) than a simple cell on the tape of a Turing machine.

To get a feel for the scales involved, consider that the information capacity of 60 qubits extends that of the classical storage capacity of all the atoms in the known universe because the dimensionality of the associated Hilbert space scales exponentially (which would be 2⁶⁰ for 60 qubits).

Nevertheless, quantum computers are tricky to build and tricky to program. Quantum states have a tendency to decohere and get entangled with everything in the environment that can’t run away from them fast enough.

It is also not yet clear how useful quantum computers will actually be in the long run, although it is too fantastic a buzzword not to throw them around at the watercooler every now and then (or jump on the bandwagon and write Medium articles about them…), and whether they will replace classical computers in any significant way.

Theoretical physicist Leonard Susskind claims here that the main area of application for quantum computers might simply lie in simulating quantum systems. This is really exciting for theoretical physicists and could provide very useful applications in quantum chemistry and condensed matter/many-body physics, but would not transform the way we use computers in our daily lives. Another application is quantum cryptography (read here for a great introduction), which might provide its uses but also won’t put all of our lives onto their respective heads (frankly, we don’t seem to care too much about our privacy today anyway).

A Question of Scale

The scale of quantum physics is related to the Planck constant. The Planck constant h is tiny. It is so tiny that it took mankind until around 100 years ago to even notice it. Because h is so tiny, it’s really hard to realize that there is something wrong with our intuitions about the nature of physics, which evolved in the world of apes throwing stones at animals in the savannah.

If you throw a stone at a gazelle and its trajectory diverges around 10⁵⁰ centimeters from the classical, intended trajectory, you are still more like to assume your aim was off because you didn’t get enough sleep after the shaman told one to many stories around the campfire the night before and not because some quantum effect kicked in.

But alas, we have come a long way and are now (metaphorically) throwing protons into each other. At these scales quantum effects really become important, allowing us to examine the laws of quantum physics in more and more depth.

Classical Computers in a Quantum Universe

The correspondence principle, first formulated by Nils Bohr, states that every quantum theory has to correspond to a classical theory in the limes of large distances because this classical theory is precisely what we observe as beings existing on these larger scales.

Point being: a classical-looking universe can be, and is to some extent implemented within a quantum universe when you zoom out(even though we have since discovered macroscopic quantum effects, such as Bose-Einstein-condensates).

The world really looks very classical in almost every aspect of our lives, and even though the universe is quantum deep down, a lot of classical-looking things can take place in it. One consequence of this is that you can implement classical computers in a quantum world.

In a slightly confusing turn of events, most of our modern classical computers still rely on quantum physics: you could not understand or build a transistor without quantum effects being taken into account. Nevertheless, transistors implement classical Turing machines by encoding information in classical bits. As mankind has come to see, it’s much easier to build a classical computer than a quantum computer (if you are not convinced, look at what has been going on for the last 80 years).

This gives reason to believe that the organ that allows us to “compute” the world might be classical as well.

The Brain as a Classical Computer

Quantum computers have to deal with all kinds of problems that classical computers don’t have. One is known in quantum physics as decoherence. Wave functions are fickle things. They like to spread out and get entangled to all kinds of other things from the outside of the quantum system. Keeping the wave function of the qubits, in which your information is stored in a quantum system, from decohering, is a really really difficult engineering problem, as adding error correction is far from trivial, while in the classical Turing machine, a simple piece of paper can reliably carry information forward in time.

To build a quantum system that stores information and manipulates it with qubits is an engineering challenge that messy mother nature would probably have a hard time implementing through incremental, random changes, and considering the time-scales involved in neural computation, and the fact that it is going on at room temperature, people like Max Tegmark have argued that decoherence time scales are far too small for them to play any role in the brain.

This for me is the most convincing argument that the brain is indeed a classical computer in every aspect that counts (again noting that I can’t get here into the debate about in which sense the brain can be thought of as a Turing machine).

We are not entirely sure how information is stored and processed in the brain (see my article on Ants and the Problems with Neural Networks), but using qubits as the atoms of information storage and information processing would be quite surprising.

Nevertheless, this does not mean that quantum effects might not still play a role in the brain and when it comes to grasping the c-word. Natural phenomena like photosynthesis have been hotly debated to rely on quantum coherence, although it looks like this might not be as much the case as expected.

But the fact remains that photosynthesis can not be explained without quantum physics. After all, the universe is quantum deep down, and as long as we don’t fully understand the brain and its most mysterious product, consciousness, there is room for new theories.

Interpreting Quantum Mechanics

“If you could blow the brain up to the size of a mill and walk about inside, you would not find consciousness.”
Gottfried Wilhelm Leibniz

Leibniz surely did not anticipate quantum physics, but quantum physics shows us that scales can become relevant.

Quantum physics is notoriously difficult to interpret (I wrote this and this article going into it in much more detail). In the Kopenhagen interpretation of quantum physics, observers cause the collapse of wave functions by measuring it and forcing the wave function into an eigenstate of an observable. In Von Neumann’s Mathematical Foundations of Quantum Mechanics, he speculatively calls this observer that ends the chain of observation the “abstract ego” (read here about his theory and connections to the role of mind). On the other hand, in the Many World Interpretation, every outcome of a quantum measurement is realized simultaneously, because the observer itself is treated as a quantum system, and therefore gets entangled to the wave function of the quantum system that is measured.

Schroedinger’s synaptic cleft

The Hodgin-Huxley-Model of the neuron describes the generation of an action potential by a single neuron, based on potassium and sodium conductances and reversal potentials and leak conductances in the synaptic cleft.

The neuron either fires if it gets pushed above a certain threshold, or it doesn’t fire if it stays below the threshold (in neural networks, this is modeled through the activation function, which introduces nonlinearities into the system). This model describes the neuron as a dynamical system, and dynamical systems can have so-called bifurcations. In this case, this means the neuron either fires or doesn’t depending on some small change in the synaptic cleft.

Keep in mind synaptic clefts are very small. The ions flowing in the synaptic channel are treated classically in the Hodgin-Huxley-Model models, but is this legitimate? Now not only every neuron, but the whole brain is a complex nonlinear dynamical system and, as this paper points out, in these kinds of systems, microscopic fluctuations can blow up and influence global behavior, which in turn might be exploited for neuronal computation.

But the synaptic cleft also raises a philosophical question: In Schrödinger’s famous thought experiment, a cat is thought of being dead and alive at the same time before an observer measures her quantum state and forces her fate. Applying this thought experiment to the brain, could neurons be in a superposition of firing and not firing at the same time if the neurotransmitters are treated as quantum systems, potentially affecting the global state of the brain?

And to add a philosophical dimension: when we talk about observers in a theory, we implicitly assume that these observers are constituted by brains. When it comes to making measurements in the brain’s synapses itself, where would an observer even come from, and how does this relate to the debate about the Kopenhagen Interpretation and the Many World Interpretation?

Quantum Theories of the Mind

As these kinds of questions still loom large and unanswered, several high-profile scientists have come to speculate if quantum effects might be necessary to explain what is going on in the brain.

As has been clear since the 1930s, quantum theory is non-local. In entangled quantum systems, part of the information lives in the entanglement itself, which is not stored locally. As consciousness appears to us as a unified, non-local field (also known as the binding-problem in the philosophy of consciousness) it is hard for us to imagine it coming from billions of individual neurons, which makes it tempting to draw the conclusion that consciousness could arise from or be connected to quantum effects. But keep in mind that this is as of yet merely a metaphorical statement: it does in no way necessitate that the binding problem can only be explained by the non-locality of quantum theory.

Another famous controversial example is Penrose’s and Hammeroff’s Orch OR theory, which postulates how quantum states are reduced within the neurons by so-called microtubules. The theory is rather complex and would go beyond the scope of this article (the Stanford Encyclopedia of Philosophy article on Quantum Approaches to Consciousness gives a more detailed overview). It has been much debated and probably doesn’t hold, but is nevertheless an interesting impulse.

I still think it is important to emphasize that these theories are speculations, have varying degrees of sophistication, and have not been confirmed in any experimental framework.

But on the other hand, there is still some space to explain what happens in the brain, how consciousness comes about and how it interacts with quantum physics, so there is reason to remain curious and open about what the future will bring, and to wait for everything that I wrote about in the first half of this article to be proven wrong.

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